Misuse of Obreshkov-like numerical integrators as numerical differentiators may lead to numerical oscillation or bias. Criteria for Obreshkov-like numerical integrators to be used as numerical differentiators are proposed in this paper to avoid these misleading phenomena. The coefficients of a numerical integrator for the highest order derivative turn out to determine its suitability. Some existing Obreshkov-like numerical integrators are examined under the proposed criteria. It is revealed that the notorious numerical oscillations induced by the implicit trapezoidal method cannot always be eliminated by using the backward Euler method for a few time steps. Guided by the proposed criteria, a frequency response optimized integrator considering second order derivative is put forward which is suitable to be used as a numerical differentiator. Theoretical observations are demonstrated in time domain via case studies.

翻译：将Obreshkov类数字集成器误用为数字差异器可能导致数字振荡或偏差。本文件建议了Obreshkov类数字集成器用作数字差异器的标准,以避免这些误导现象。最高顺序衍生物的数字集成器系数可以用来确定其是否合适。一些现有的Obreshkov类数字集成器根据拟议标准加以审查。人们发现,通过使用落后的Euler 方法在几个时间步骤中不能总是消除由隐含的捕捉灭虫方法引起的臭名昭著的数字振荡器。在拟议标准的指导下,提出一个考虑到第二顺序衍生物的频率优化集成器,适合用作数字差异器。通过案例研究在时间域显示理论观察。